Almost all the public key encryption and identification schemes proposed so far are based on modular multiplications with a modulus n which is the product of two secret primes p and q. To make the factorization of n difficult, it is necessary to use very large numbers. The minimum recommended size of n is currently 512 bits, but due to the explosive growth of computing power available to cryptanalysts, this minimum size is likely to increase to 1024 bits (and to even larger values for high security applications).
In many communication and access control applications, it is desirable to use smart cards to carry out sensitive computations. Among the many reasons for this choice are the small physical size, the portability, the non-volatile memory, and the security offered by a single chip computer embedded in a plastic card. Millions of smart cards are used each year to make bank cards more secure, to control access to pay-TV, to carry billing information in cellular telephones, etc.
The biggest limitation in today's smart cards is the small amount of random access memory (RAM) available in the card. The most popular smart card chip made by Motorola has 36 bytes of RAM, and the most popular smart card chip made by Thomson has 44 bytes of RAM. This should be compared with the 4 million bytes of RAM available in a typical personal computer.
Some algorithms can make use of other types of memory: A typical smart card contains several thousand bytes of ROM and several thousand bytes of EEPROM. ROM is unchangeable, and typically stores the program which controls the operation of the smart card. EEPROM is changeable, but writing into it is about one thousand times slower than writing into RAM and the number of times a bit can be rewritten cannot exceed 10,000. It is thus possible to use EEPROM to store slowly changing data such as cryptographic keys or the details of financial transactions, but not as a RAM substitute for intermediate values in a long computation.